2016/01/10

# SICP 問題 4.34

consへのタグづけがどうしてもうまくいかなくてここを参考にしました．

SICP Exercise 4.34 | Weiqun Zhang's Blog

``````(define (eval exp env)
(cond ((self-evaluating? exp) exp)
((variable? exp) (lookup-variable-value exp env))
((quoted? exp) (eval-quote exp env))
((assignment? exp) (eval-assignment exp env))
((definition? exp) (eval-definition exp env))
((if? exp) (eval-if exp env))
((lambda? exp)
(make-procedure (lambda-parameters exp)
(lambda-body exp)
env))
((list-lambda? exp) ;;list-lambda?とmake-list-procedureの追加
(make-list-procedure (lambda-parameters exp)
(lambda-body exp)
env))
((let? exp) (eval (let->combination exp) env))
((let*? exp) (eval (let*->nested-lets exp) env))
((letrec? exp) (eval (letrec->let exp) env))
((begin? exp)
(eval-sequence (begin-actions exp) env))
((cond? exp) (eval (cond->if exp) env))
((and? exp) (eval-and exp env))
((or? exp) (eval-or exp env))
((application? exp)
(my-apply (actual-value (operator exp) env)
(operands exp)
env))
(else
(error "Unknown expression type --EVAL" exp))))

;; 追加
(define (list-lambda? exp) (tagged-list? exp 'list-lambda))
(define (make-list-procedure parameters body env)
(list 'list-proc parameters (scan-out-defines body) env))

;; list-procに対応
(define (compound-procedure? p)
(or (tagged-list? p 'procedure)
(tagged-list? p 'list-proc)))

;; cons,car,cdrを削除
(define primitive-procedures
(list (list 'null? null?)
(list '= =)
(list '- -)
(list '+ +)
(list '* *)
(list '/ /)
(list 'newline newline)
(list 'display display)
(list '() '())))

;; list-procの時はlist-display
(define (user-print object)
(cond ((tagged-list? object 'list-proc)
(list-display (match-to object)))
((compound-procedure? object)
(display (list 'compound-procedure
(procedure-parameters object)
(procedure-body object)
'<procedure-env>)))
(else (display object))))

;; 以下はlist-displayのための手続き
(define (match-to obj)
(match obj
((procedure (m) body ((parameters exp1 exp2) env))
(cons exp1 exp2))))

(define (first-list-value exp)
(display (force-it (car exp))))

(define (list-display exp)
(list-display-iter exp 10))

(define (list-display-iter exp n)
(cond ((= n 0)
(display "...)"))
(else (when (= n 10)
(display "("))
(continue-display exp n))))

(define (continue-display exp n)
(first-list-value exp)
(let ((second (force-it (cdr exp))))
(cond ((null? second) (display ")"))
((or (self-evaluating? second) (symbol? second))
(display " . ")
(display second)
(display ")"))
(else (display " ")
(list-display-iter (match-to second) (- n 1))))))

;; 遅延リスト用の手続き
(actual-value
'(begin (define (cons x y)
(list-lambda (m) (m x y)))
(define (car z)
(z (lambda (p q) p)))
(define (cdr z)
(z (lambda (p q) q)))

(define (list-ref items n)
(if (= n 0)
(car items)
(list-ref (cdr items) (- n 1))))

(define (map proc items)
(if (null? items)
'()
(cons (proc (car items))
(map proc (cdr items)))))

(define (scale-list items factor)
(map (lambda (x) (* x factor))
items))

(cond ((null? list1) list2)
((null? list2) list1)
(else (cons (+ (car list1) (car list2))
(define ones (cons 1 ones))

(define integers (cons 0 (add-lists ones integers)))

(define (integral integrand initial-value dt)
(define int
(cons initial-value
int)))
int)

(define (solve f y0 dt)
(define y (integral dy y0 dt))
(define dy (map f y))
y)

)
the-global-environment)
``````

test

``````;;; M-Eval input:
ones

;;; M-Eval value:
(1 1 1 1 1 1 1 1 1 1 ...)

;;; M-Eval input:
(cons 1 2)

;;; M-Eval value:
(1 . 2)

;;; M-Eval input:
(cons 'a (cons 'b (cons 'c 'd)))

;;; M-Eval value:
(a b c . d)

;;; M-Eval input:
(cons 'a (cons 'b (cons 'c '())))

;;; M-Eval value:
(a b c)

;;; M-Eval input:
integers

;;; M-Eval value:
(0 1 2 3 4 5 6 7 8 9 ...)

;;; M-Eval input:
'(1 2 3)

;;; M-Eval value:
(1 2 3)

;;; M-Eval input:
'()

;;; M-Eval value:
()

;;; M-Eval input:
(cons '() '())

;;; M-Eval value:
(())
``````

``````(use util.match)
(define true #t)
(define false #f)

(define (eval exp env)
(cond ((self-evaluating? exp) exp)
((variable? exp) (lookup-variable-value exp env))
((quoted? exp) (eval-quote exp env))
((assignment? exp) (eval-assignment exp env))
((definition? exp) (eval-definition exp env))
((if? exp) (eval-if exp env))
((lambda? exp)
(make-procedure (lambda-parameters exp)
(lambda-body exp)
env))
((list-lambda? exp) ;;list-lambda?とmake-list-procedureの追加
(make-list-procedure (lambda-parameters exp)
(lambda-body exp)
env))
((let? exp) (eval (let->combination exp) env))
((let*? exp) (eval (let*->nested-lets exp) env))
((letrec? exp) (eval (letrec->let exp) env))
((begin? exp)
(eval-sequence (begin-actions exp) env))
((cond? exp) (eval (cond->if exp) env))
((and? exp) (eval-and exp env))
((or? exp) (eval-or exp env))
((application? exp)
(my-apply (actual-value (operator exp) env)
(operands exp)
env))
(else
(error "Unknown expression type --EVAL" exp))))

;; メモ化する評価器
(define (force-it obj)
(cond ((thunk? obj)
(let ((result (actual-value (thunk-exp obj)
(thunk-env obj))))
(set-car! obj 'evaluated-thunk)
(set-car! (cdr obj) result) ;;expをその値で置き換える
(set-cdr! (cdr obj) '())    ;;必要のなくなったenvを忘れる
result))
((evaluated-thunk? obj) (thunk-value obj))
(else obj)))

(define (delay-it exp env) (list 'thunk exp env))
(define (thunk? exp) (tagged-list? exp 'thunk))

(define (evaluated-thunk? obj) (tagged-list? obj 'evaluated-thunk))

(define (actual-value exp env)
(force-it (eval exp env)))
(define (foo bar)
(bar 'a))

;; apply
(define (my-apply procedure arguments env)
(cond ((primitive-procedure? procedure)
(apply-primitive-procedure
procedure
(list-of-arg-values arguments env))) ; changed
((compound-procedure? procedure)
(eval-sequence
(procedure-body procedure)
(extend-environment (procedure-parameters procedure)
(list-of-delayed-args arguments env) ; changed
(procedure-environment procedure))))
(else (error "Unknown procedure type: APPLY" procedure))))

(define (list-of-arg-values exps env)
(if (no-operands? exps)
'()
(cons (actual-value (first-operand exps) env)
(list-of-arg-values (rest-operands exps) env))))

(define (list-of-delayed-args exps env)
(if (no-operands? exps)
'()
(cons (delay-it (first-operand exps) env)
(list-of-delayed-args (rest-operands exps) env))))

(define (eval-if exp env)
(if (true? (actual-value (if-predicate exp) env))
(eval (if-consequent exp) env)
(eval (if-alternative exp) env)))

;; 並び
(define (eval-sequence exps env)
(cond ((last-exp? exps) (eval (first-exp exps) env))
(else (eval (first-exp exps) env)
(eval-sequence (rest-exps exps) env))))

;; 代入
(define (eval-assignment exp env)
(set-variable-value! (assignment-variable exp)
(eval (assignment-value exp) env)
env)
'ok)

;; 定義
(define (eval-definition exp env)
(define-variable!
(definition-variable exp)
(eval (definition-value exp) env)
env)
'ok)

;; 自己評価式
(define (self-evaluating? exp)
(cond ((number? exp) true)
((string? exp) true)
(else false)))

;; 変数
(define (variable? exp) (symbol? exp))

;; クオート
(define (quoted? exp)
(tagged-list? exp 'quote))

(define (make-quote obj)
(list 'quote obj))
(define (eval-quote exp env)
(let ((obj (quote-body exp)))
(cond ((null? obj) obj)
((symbol? obj) obj)
((self-evaluating? obj) obj)
(else (eval (quote->cons obj) env)))))

(define (quote->cons obj)
(cond ((null? obj) (make-quote obj))
((symbol? obj) (make-quote obj))
(else (list 'cons (make-quote (car obj))
(quote->cons (cdr obj))))))

(define (tagged-list? exp tag)
(if (pair? exp)
(eq? (car exp) tag)
false))

;; 代入
(define (assignment? exp)
(tagged-list? exp 'set!))

;; 定義
(define (definition? exp)
(tagged-list? exp 'define))

(define (definition-variable exp)

(define (definition-value exp)
(cddr exp)))) ;;本体

;; lambda式
(define (lambda? exp) (tagged-list? exp 'lambda))
(define (lambda-body exp) (cddr exp))

(define (make-lambda parameters body)
(cons 'lambda (cons parameters body)))

(define (def-body-list proc-body)
(let iter ((proc-body proc-body)
(def '())
(body '()))
(cond ((null? proc-body) (cons (reverse def) (reverse body)))
((definition? (car proc-body)) (iter (cdr proc-body)
(cons (car proc-body) def)
body))
(else (iter (cdr proc-body)
def
(cons (car proc-body) body))))))

(define (list-lambda? exp) (tagged-list? exp 'list-lambda))
(define (make-list-procedure parameters body env)
(list 'list-proc parameters (scan-out-defines body) env))

;; 4.17
(define (scan-out-defines body)
(define (split-def-body proc-body)
(let iter ((proc-body proc-body)
(def '())
(body '()))
(cond ((null? proc-body) (cons (reverse def) (reverse body)))
((definition? (car proc-body)) (iter (cdr proc-body)
(cons (car proc-body) def)
body))
(else (iter (cdr proc-body)
def
(cons (car proc-body) body))))))
(let* ((def-body-list (split-def-body body))
(def-list (car def-body-list))
(body-list (cdr def-body-list)))
(if (null? def-list)
body
(append  (map (lambda (x) (make-definition (definition-variable x) ''*unassigned*))
def-list)
(map (lambda (x) (list 'set! (definition-variable x)
(definition-value x)))
def-list)
body-list))))

;; if
(define (if? exp) (tagged-list? exp 'if))
(define (if-alternative exp)
(if (not (null? (cdddr exp)))
'false))

(define (make-if predicate consequent alternative)
(list 'if predicate consequent alternative))

;; begin
(define (begin? exp) (tagged-list? exp 'begin))
(define (begin-actions exp) (cdr exp))
(define (last-exp? seq) (null? (cdr seq)))
(define (first-exp seq) (car seq))
(define (rest-exps seq) (cdr seq))

(define (sequence->exp seq)
(cond ((null? seq) seq)
((last-exp? seq) (first-exp seq))
(else (make-begin seq))))

(define (make-begin seq) (cons 'begin seq))

;; 任意の合成式
(define (application? exp) (pair? exp))
(define (operator exp) (car exp))
(define (operands exp) (cdr exp))
(define (no-operands? ops) (null? ops))
(define (first-operand ops) (car ops))
(define (rest-operands ops) (cdr ops))

;; 派生式
(define (cond? exp) (tagged-list? exp 'cond))
(define (cond-clauses exp) (cdr exp))
(define (cond-else-clause? clause)
(eq? (cond-predicate clause) 'else))
(define (cond-predicate clause) (car clause))
(define (cond-actions clause) (cdr clause))

(define (cond->if exp)
(expand-clauses (cond-clauses exp)))

(define (expand-clauses clauses)
(if (null? clauses)
'false
(let ((first (car clauses))
(rest (cdr clauses)))
(if (cond-else-clause? first)
(if (null? rest)
(sequence->exp (cond-actions first))
(error "ELSE clause isn't last -- COND->IF" clauses))
(let ((action (cond-actions first))
(predicate (cond-predicate first)))
(make-if predicate
(if (eq? (car action) '=>)
(sequence->exp action))
(expand-clauses rest)))))))

;; and
(define (and? exp) (tagged-list? exp 'and))
(define (and-clauses exp) (cdr exp))

(define (eval-and exp env)
(let iter ((clauses (and-clauses exp)))
(if (null? clauses)
'true
(let ((first (eval (car clauses) env)))
(cond ((null? (cdr clauses)) first)
(first (iter (cdr clauses)))
(else 'false))))))

;; or
(define (or? exp) (tagged-list? exp 'or))
(define (or-clauses exp) (cdr exp))

(define (eval-or exp env)
(let iter ((clauses (or-clauses exp)))
(if (null? clauses)
'false
(let ((first (eval (car clauses) env)))
(cond ((null? (cdr clauses)) first)
(first 'true)
(else (iter (cdr clauses))))))))

;; let
(define (let? exp) (tagged-list? exp 'let))
(define (let-variables exp) (map car (let-parameters exp)))
(define (let-expressions exp) (map cadr (let-parameters exp)))
(define (let-bodys exp) (cddr exp))

(define (let->combination exp)
(if (symbol? (cadr exp)) ;; 2番目の要素がシンボルならnamed-let
(named-let->define (named-let-func-name exp)
(named-let-variables exp)
(named-let-expressions exp)
(named-let-bodys exp))
(cons (make-lambda (let-variables exp)
(let-bodys exp))
(let-expressions exp))))

;; let*
(define (let*? exp) (tagged-list? exp 'let*))
(define (let*-variables exp) (map car (let*-parameters exp)))
(define (let*-expressions exp) (map cadr (let*-parameters exp)))
(define (let*-body exp) (cddr exp))

(define (make-let parameters bodys)
(cons 'let (cons parameters bodys)))

(define (let*->nested-lets exp)
(expand-lets (let-parameters exp) (let-bodys exp)))

(define (expand-lets parameters bodys)
(cond ((null? parameters) (error "EXPAND-LETS required pair, but " parameters))
((null? (cdr parameters))
(make-let (list (car parameters))
bodys))
(else (make-let (list (car parameters))
(list (expand-lets (cdr parameters) bodys))))))

;; named-let
(define (named-let? exp) (symbol? (cadr exp)))
(define (named-let-variables exp) (map car (named-let-parameters exp)))
(define (named-let-expressions exp) (map cadr (named-let-parameters exp)))
(define (named-let-bodys exp) (cdddr exp))

(define (make-definition variable value)
(list 'define variable value))

(define (named-let->define func-name variables expressions bodys)
(make-begin (list (make-definition func-name (make-lambda variables bodys))
(cons func-name expressions))))

;; 4.20
;; 選択子
(define (letrec? exp) (tagged-list? exp 'letrec))
(define (letrec-variables exp) (map car (letrec-parameters exp)))
(define (letrec-expressions exp) (map cadr (letrec-parameters exp)))
(define (letrec-body exp) (cddr exp))

(define (letrec->let exp)
(make-let (map (lambda (x) (list x ''*unassigned*))
(letrec-variables exp))
(append (map (lambda (x y) (list 'set! x y))
(letrec-variables exp)
(letrec-expressions exp))
(letrec-body exp))))

;; 術後のテスト
(define (true? x)
(not (eq? x '#f)))
(define (false? x)
(eq? x '#f))

;; 手続きの表現
(define (make-procedure parameters body env)
(list 'procedure parameters (scan-out-defines body) env))
(define (compound-procedure? p)
(or (tagged-list? p 'procedure)
(tagged-list? p 'list-proc)))

;; 環境に対する操作
(define (enclosing-environment env) (cdr env))
(define (first-frame env) (car env))
(define the-empty-environment '())

;; フレーム
(define (make-frame variables values)
(cons variables values))
(define (frame-variables frame) (car frame))
(define (frame-values frame) (cdr frame))

(set-car! frame (cons var (frame-variables frame)))
(set-cdr! frame (cons val (frame-values frame))))

;; 変数を値に対応づける新しいフレーム
(define (extend-environment vars vals base-env)
(if (= (length vars) (length vals))
(cons (make-frame vars vals) base-env)
(if (< (length vars) (length vals))
(error "Too many arguments supplied" vars vals)
(error "Too few arguments supplied" vars vals))))

(define (lookup-variable-value var env)
(define (env-loop env)
(define (scan vars vals)
(cond ((null? vars)
(env-loop (enclosing-environment env)))
((eq? var (car vars))
(if (eq? (car vals) '*unassigned*)
(error "*Unassigned* variable" var)
(car vals)))
(else (scan (cdr vars) (cdr vals)))))
(if (eq? env the-empty-environment)
(error "Unbound variable" var)
(let ((frame (first-frame env)))
(scan (frame-variables frame)
(frame-values frame)))))
(env-loop env))

(define (set-variable-value! var val env)
(define (env-loop env)
(define (scan vars vals)
(cond ((null? vars)
(env-loop (enclosing-environment env)))
((eq? var (car vars))
(set-car! vals val))
(else (scan (cdr vars) (cdr vals)))))
(if (eq? env the-empty-environment)
(error "Unbound variable -- SET!" var)
(let ((frame (first-frame env)))
(scan (frame-variables frame)
(frame-values frame)))))
(env-loop env))

(define (define-variable! var val env)
(let ((frame (first-frame env)))
(define (scan vars vals)
(cond ((null? vars)
((eq? var (car vars))
(set-car! vals val))
(else (scan (cdr vars) (cdr vals)))))
(scan (frame-variables frame)
(frame-values frame))))

(define (primitive-procedure? proc)
(tagged-list? proc 'primitive))

(define primitive-procedures
(list (list 'null? null?)
(list '= =)
(list '- -)
(list '+ +)
(list '* *)
(list '/ /)
(list 'newline newline)
(list 'display display)
(list '() '())))

(define (primitive-procedure-names)
(map car primitive-procedures))

(define (primitive-procedure-objects)
(map (lambda (proc) (list 'primitive (cadr proc)))
primitive-procedures))

(define (apply-primitive-procedure proc args)
(apply-in-underlying-scheme
(primitive-implementation proc) args))

(define apply-in-underlying-scheme apply)

;; 環境
(define (setup-environment)
(let ((initial-env
(extend-environment (primitive-procedure-names)
(primitive-procedure-objects)
the-empty-environment)))
(define-variable! 'true #t initial-env)
(define-variable! 'false #f initial-env)
initial-env))

(define the-global-environment (setup-environment))

(define input-prompt ";;; M-Eval input:")
(define output-prompt ";;; M-Eval value:")

(define (driver-loop)
(prompt-for-input input-prompt)
(let ((output (actual-value input the-global-environment)))
(announce-output output-prompt)
(user-print output)))
(driver-loop))

(define (prompt-for-input string)
(newline)
(newline)
(display string)
(newline))

(define (announce-output string)
(newline)
(display string)
(newline))

(define (user-print object)
(cond ((tagged-list? object 'list-proc)
(list-display (match-to object)))
((compound-procedure? object)
(display (list 'compound-procedure
(procedure-parameters object)
(procedure-body object)
'<procedure-env>)))
(else (display object))))

(define (match-to obj)
(match obj
((procedure (m) body ((parameters exp1 exp2) env))
(cons exp1 exp2))))

(define (first-list-value exp)
(display (force-it (car exp))))

(define (list-display exp)
(list-display-iter exp 10))

(define (list-display-iter exp n)
(cond ((= n 0)
(display "...)"))
(else (when (= n 10)
(display "("))
(continue-display exp n))))

(define (continue-display exp n)
(first-list-value exp)
(let ((second (force-it (cdr exp))))
(cond ((null? second) (display ")"))
((or (self-evaluating? second) (symbol? second))
(display " . ")
(display second)
(display ")"))
(else (display " ")
(list-display-iter (match-to second) (- n 1))))))

(actual-value
'(begin (define (cons x y)
(list-lambda (m) (m x y)))
(define (car z)
(z (lambda (p q) p)))
(define (cdr z)
(z (lambda (p q) q)))

(define (list-ref items n)
(if (= n 0)
(car items)
(list-ref (cdr items) (- n 1))))

(define (map proc items)
(if (null? items)
'()
(cons (proc (car items))
(map proc (cdr items)))))

(define (scale-list items factor)
(map (lambda (x) (* x factor))
items))

(cond ((null? list1) list2)
((null? list2) list1)
(else (cons (+ (car list1) (car list2))
(define ones (cons 1 ones))

(define integers (cons 0 (add-lists ones integers)))

(define (integral integrand initial-value dt)
(define int
(cons initial-value
int)))
int)

(define (solve f y0 dt)
(define y (integral dy y0 dt))
(define dy (map f y))
y)

)
the-global-environment)
``````